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001 978-3-319-27526-0
003 DE-He213
005 20181204134229.0
007 cr nn 008mamaa
008 160923s2016 gw | s |||| 0|eng d
020 _a9783319275260
_9978-3-319-27526-0
024 7 _a10.1007/978-3-319-27526-0
_2doi
040 _aISI Library, Kolkata
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
072 7 _aPBKJ
_2thema
082 0 4 _a515.353
_223
100 1 _aStenger, Frank.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aNavier–Stokes Equations on R3 × [0, T]
_h[electronic resource] /
_cby Frank Stenger, Don Tucker, Gerd Baumann.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2016.
300 _aX, 226 p. 25 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPreface -- Introduction, PDE, and IE Formulations -- Spaces of Analytic Functions -- Spaces of Solution of the N–S Equations -- Proof of Convergence of Iteration 1.6.3 -- Numerical Methods for Solving N–S Equations -- Sinc Convolution Examples -- Implementation Notes -- Result Notes.
520 _aIn this monograph, leading researchers in the world of numerical analysis, partial differential equations, and hard computational problems study the properties of solutions of the Navier–Stokes partial differential equations on (x, y, z, t) ∈ ℝ3 × [0, T]. Initially converting the PDE to a system of integral equations, the authors then describe spaces A of analytic functions that house solutions of this equation, and show that these spaces of analytic functions are dense in the spaces S of rapidly decreasing and infinitely differentiable functions. This method benefits from the following advantages: The functions of S are nearly always conceptual rather than explicit Initial and boundary conditions of solutions of PDE are usually drawn from the applied sciences, and as such, they are nearly always piece-wise analytic, and in this case, the solutions have the same properties When methods of approximation are applied to functions of A they converge at an exponential rate, whereas methods of approximation applied to the functions of S converge only at a polynomial rate Enables sharper bounds on the solution enabling easier existence proofs, and a more accurate and more efficient method of solution, including accurate error bounds Following the proofs of denseness, the authors prove the existence of a solution of the integral equations in the space of functions A ∩ ℝ3 × [0, T], and provide an explicit novel algorithm based on Sinc approximation and Picard–like iteration for computing the solution. Additionally, the authors include appendices that provide a custom Mathematica program for computing solutions based on the explicit algorithmic approximation procedure, and which supply explicit illustrations of these computed solutions.
650 0 _aDifferential equations, partial.
650 1 4 _aPartial Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12155
700 1 _aTucker, Don.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aBaumann, Gerd.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319275246
776 0 8 _iPrinted edition:
_z9783319275253
776 0 8 _iPrinted edition:
_z9783319801629
856 4 0 _uhttps://doi.org/10.1007/978-3-319-27526-0
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c426560
_d426560